A conventional round, small connector socket disclosed in U.S. Pat. No. 4,637,669 has an electromagnetic shield and relatively firmly holds the mating plug put therein, but since no locking mechanism is provided, the plug may sometimes come out of the socket when the plug cable is pulled inadvertently. In U.S. Pat. No. 4,548,455 (reissued as U.S. Pat. No. 32,864) there is disclosed a connector plug with a lock which is capable of preventing easy disengagement from the socket, but no proposal has been made of a socket with a lock which is suitable for use with an electromagnetically shielded connector plug with a lock.